{
  "id": "0805.3731",
  "version": "v1",
  "published": "2008-05-23T23:50:41.000Z",
  "updated": "2008-05-23T23:50:41.000Z",
  "title": "Three dimensional C-, S- and E-transforms",
  "authors": [
    "M. Nesterenko",
    "J. Patera"
  ],
  "comment": "24 pages, 13 figures",
  "doi": "10.1088/1751-8113/41/47/475205",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Three dimensional continuous and discrete Fourier-like transforms, based on the three simple and four semisimple compact Lie groups of rank 3, are presented. For each simple Lie group, there are three families of special functions ($C$-, $S$-, and $E$-functions) on which the transforms are built. Pertinent properties of the functions are described in detail, such as their orthogonality within each family, when integrated over a finite region $F$ of the 3-dimensional Euclidean space (continuous orthogonality), as well as when summed up over a lattice grid $F_M\\subset F$ (discrete orthogonality). The positive integer $M$ sets up the density of the lattice containing $F_M$. The expansion of functions given either on $F$ or on $F_M$ is the paper's main focus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-23T23:50:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33-02",
      "33E99",
      "42B99",
      "42C15",
      "58C40"
    ],
    "keywords": [
      "dimensional",
      "semisimple compact lie groups",
      "e-transforms",
      "papers main focus",
      "simple lie group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Nov",
      "volume": 41,
      "number": 47,
      "pages": 475205
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41U5205N"
    }
  }
}